Robust finite-time control approach for spacecraft rendezvous and formation reconfiguration in Earth orbits

ABSTRACT This paper investigates the optimal control problem for spacecraft formation with predefined performance by proposing a sliding mode controller based on the State‐Dependent Riccati Equation (SDRE) method. First, a controller with an adjustable variable is designed using sliding mode control theory, aimed at minimizing formation error, reducing energy consumption, and optimizing the convergence process of the sliding surface. To manage the predefined performance constraints, a nonlinear function related to these constraints is directly incorporated into the controller and optimal performance index function, simplifying the computations involved. Next, the sliding surface is introduced into the system equations as an extended state to enhance the system's disturbance rejection capability. The adjustable variables on the sliding surface are obtained by applying the SDRE method. Finally, simulations demonstrate that the controller effectively achieves optimal control of spacecraft formation while meeting the predefined performance criteria.

This paper presents a distributed motion planning framework for safely reconfiguring spacecraft formations to desired configurations. A control Lyapunov function based guidance strategy is developed to guarantee convergence while satisfying control rate constraints. To ensure collision avoidance during maneuvering, a high-order control barrier function based approach is integrated to impose safety constraints between spacecraft. Actuator saturation is explicitly handled by incorporating output constraints into the control design. The overall guidance and planning problem is formulated as a constrained quadratic programming problem, which yields optimal, collision-free trajectories in real time. Simulation results demonstrate that the proposed method enables safe and efficient formation reconfiguration without compromising convergence or violating actuator limits. • A new method enables safe and efficient reconfiguration of spacecraft formations. • The guidance direction is designed using a smooth 3D vector field. • Safety and stability are ensured by combining guidance with safety constraints. • Real-time collision-free paths are computed using an optimization-based approach.

Machine learning-aided adaptive control of spacecraft formation path planning and collision avoidance

This paper investigates the adaptive optimal enclosure control problem for multi-spacecraft systems surrounding a noncooperative target. Based on the orbital dynamics derived from the two-body problem, a manifold-based invariant estimation method is developed to accurately reconstruct the unknown control input of the target. Subsequently, a dynamic model of relative orbital error is established to formulate the enclosure control objective. An adaptive dynamic programming (ADP) approach utilizing a single critic neural network is proposed to approximate the solution of the Hamilton–Jacobi–Bellman (HJB) equation online. To alleviate onboard computational burdens, an adaptive event-triggered mechanism incorporating a dynamic state regulator (DSR) and an auxiliary threshold modulator (ATM) is designed, which actively adjusts the triggering threshold to balance triggering frequency and control accuracy. Thus, an event-driven weight update law is further introduced, significantly reducing the update rate while maintaining satisfactory approximation performance. The resulting optimal control law ensures precise enclosure formation with guaranteed stability. The uniform ultimate boundedness (UUB) of the closed-loop system is rigorously proven via Lyapunov theory. Numerical simulations validate the effectiveness and efficiency of the proposed control strategy.

This paper addresses the challenge of maintaining Coulomb thrusting, a propellant-free propulsion method, in close-formation spacecraft platforms subject to perturbations such as Earth’s J 2 effect and solar radiation pressure. Although Coulomb formations offer advantages such as low propellant consumption, rapid throttling, and plume avoidance, their performance is highly sensitive to dynamic disturbances. To overcome these limitations, this paper proposes a robust optimal sliding mode control framework that reconfigures deputy spacecraft along invariant manifolds through active charge modulation of the chief spacecraft. By integrating a linear quadratic regulator with sliding-mode control, the method synthesizes a hybrid feedback law to suppress disturbances and address thruster saturation. Additionally, a Poincaré map is employed to design low-energy transfer trajectories utilizing the geometric properties of stable/unstable manifolds near collinear equilibrium points. Extensive simulations demonstrate centimeter-level tracking precision and minimal thrust requirements under charge constraints, validating the method’s robustness, optimality, and applicability to space missions.

This paper is concerned with the periodic eventtriggered (PET) control problem for spacecraft formation flying near asteroids. First, considering the limited sensing ability of the member spacecraft, an artificial potential function is incorporated to design a distributed error surface with connectivity preservation. Especially, by using the prescribed performance control technique, the convergence behavior of the proposed manifold can be actively adjusted. Then, a distributed eventtriggered formation control law is designed based on the error surface. The controller inherits the properties of the proposed error variable, which would bring convenience to the theoretical analysis of the system performance. After that, the updating frequency of the proposed controller is further reduced by taking advantage of the PET strategy. Different from the continuous event-triggered mechanism, the triggering condition in the PET mechanism only needs to be evaluated by each spacecraft at the predetermined periodic sample instants, which is more feasible to be implemented onboard the spacecraft. Besides, the relationship between the state convergence region and the sampling period is analyzed. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method. The simulation results show that the developed control strategy would enable the formation system to achieve the desired configuration with connectivity preservation, adjustable performance, and low-frequency control executions.

This paper is devoted to investigating the distributed constrained attitude coordination control problem for flexible spacecraft formation on SO(3) subject to external disturbances, actuator faults, and channel noise without modal variable measurement. Specifically, based on the Itô formula and fixed-time control approach, a distributed attitude observer is proposed to estimate the leader's states for the followers under channel noise environments in a fixed time in probability. Then the attitude constraints are handled by constructing an artificial potential function (APF) on SO(3). A distributed adaptive fault-tolerant control law is presented to achieve constrained attitude coordination by using the APF and the estimations of the leader's states and the unmeasurable modal variables. The separation principle between the distributed attitude observer and the proposed control law is adopted to prove the control law convergence. Simulation results are presented to demonstrate the theoretical findings.

Low-cost missions are ideal for applications that require spacecraft formation flying. The use of GNSS signals provides an economical solution to determine the orbital status of the formation. This paper facilitates the development of such missions by simulating spacecraft orbital formation conditions through the use of software-defined radio to generate the GNSS signals being received by each spacecraft. The simulation environment integrates low-cost commercial GNSSs, one for each member of the formation, to capture the signals generated. The analysis of the recorded raw signals shows that the instrumental error of the receivers is predominant because they have not been designed to work in orbital conditions. In addition to noise, the bias errors introduced must be taken into account by the mathematical trilateration methods, which can be very sensitive to these errors. This paper shows how sensitivity can be quantified using the condition number for matrix inversion. A condition number analysis determines that the optimal solution for trilaterating the orbital position of a spacecraft should use as few GNSS satellites as possible. The paper also introduces how to use the condition number to evaluate different methods for determining the state of the spacecraft formation: the independent trilateration method, the difference method, and the double difference method. The comparison of the methods shows that the difference and double difference methods are more sensitive to instrumental errors, because they are worse conditioned, but can be improved by reducing their order. Despite the limitations shown, at best, errors in the relative positions of the spacecrafts of the order of metres are obtained, demonstrating the feasibility of this type of mission and the usefulness of the condition number analysis method presented.

In this paper, a distributed economic nonlinear model predictive control (DENMPC) is proposed to decrease the energy consumption in attitude cooperative control of spacecraft formation flying. Unlike traditional state-based control methods, which rely on current states, the proposed DENMPC leverages the spacecraft formation flying dynamics model to incorporate forward-looking capabilities, enabling more precise cooperative control. Additionally, compared to centralized control schemes, DENMPC reduces computational complexity within the leader–follower framework, making it better suited for large-scale spacecraft formations. By constructing a fuel optimization objective function to express the characteristics of energy consumption in attitude maneuvers, the neighboring follower spacecraft information is incorporated as pseudodecision variables. The DENMPC achieves an energy-efficient cooperative attitude maneuver while improving the consistency of attitude coordination among spacecraft agents. Numerical simulations demonstrate that DENMPC reduces fuel consumption by 58% for leader spacecraft and 65% for followers, outperforming proportional derivative (PD) control, sliding mode control, and distributed model predictive control in fuel efficiency and spacecraft formation coordination.

Distributed control for spacecraft formation near irregular asteroids via quantized information exchange

ABSTRACTA data‐based fault‐tolerant controller for spacecraft formation flying (SFF) under external disturbances and actuator faults is proposed in this paper. The overall controller is based on off‐policy integral reinforcement learning (IRL) and an adaptive control strategy. First, a model‐free optimal controller is designed for the nominal healthy SFF system to track a class of reference trajectories. Second, a data‐driven fault‐tolerant controller is introduced by incorporating an adaptive approach for SFF when faced with external disturbances and actuator faults. Subsequently, the superiority of the proposed method in this paper is demonstrated and compared with the existing model‐based control algorithm. Finally, the simulation results of a typical SFF system verify the efficiency of the proposed overall control approach.

This article is concerned with the design of a leader-follower controller for attitude coordination control in spacecraft formations under directed graphs. Several common sources of unknown dynamics, including external disturbance, inertia uncertainty, and actuator saturation, are taken into account to enhance the realism of the results. First, a parametric linearization approach, guided by the fully-actuated system approach is presented to transform the original nonlinear model of each spacecraft into a linear one. Second, state estimators are developed for the followers to estimate the leader's state, with adaptive gains applied to regulate the coupling strengths among the followers. Third, by incorporating online Gaussian process regressions for uncertainty learning, a coordination controller is designed to ensure the asymptotic stability of the overall closedloop system. Finally, the effectiveness of the proposed method is validated through numerical simulations

Research on Micro-Thrust Maneuvering Strategies for Mass Center Identification in Spacecraft Formations for Gravitational Wave Detection

Nonlinear $${\mathcal {H}}_\infty $$ control for spacecraft formation flight

Optimal spacecraft trajectory and formation control for asteroid deflection using pseudo-spectral methods and halo orbits

Adaptive robust fault-tolerant attitude control for spacecraft formation with input saturation and disturbances

The Lorentz force-based control of a spacecraft formation flying using the harmonic charging law

Adaptive event-triggered attitude cooperative control for spacecraft formation with minimum inter-event times

Collaborative Covert Trajectory Planning for Spacecraft Formation Based on Configuration Transformation and Maintenance